Dislocation core-core interaction and Peierls stress in a model hexagonal lattice

A series of atomistic calculations is performed in order to explore dislocation core-core interactions and the Peierls stress in a model hexagonal lattice. The method of calculation is the lattice Green's function method, using several pair potentials with variable parameters. We confirm that dislocation cores broaden as a pair of dislocations with opposite sign move closer to each other. Continuum theories are surprisingly accurate in describing the dislocation-dislocation interaction force even in the range of strong core-core overlap. However, our atomistic calculations show that while the relation between the Peierls stress and dislocation width is exponential as the Peierls-Nabarro model predicts, that model underestimates the Peierls stress by nearly a factor of 10⁴.